So there’s two variations to this, one is a circular playmat that has a cord running around the outside, you simply lift up the by the cord and it collapses the playmat into a “sack”. The second is a rectangular playmat with hard cardboard like surfaces underneath that folds up into a box, and latches shut.
The idea with both of these is that it’s quick and easy to tidy up after your kid. They make a big mess, you basically chuck everything onto the mat, and pick it up by the cord and hang it up – tidy. To get the toys out, just drop it on the floor and it’ll unfold.
Variants of this exist: http://www.instructables.com/id/Toy-Bag-and-Play-Mat-in-One/ but you could improve on their design – e.g. using something like tent poles so that it’s tensioned so that it folds out really nicely when you untie it. I also like the box variant because box’s are much easier to fit in a room. So it could look like a chest, but then you unclip it and it folds out to be a playmat.